Two trucks to Atlanta

Question

two trucks bound for atlanta both depart from Philadelphia at the same time and travel along the same route. the first truck travels 12 miles per hour faster than the second truck and arrives 4 hours earlier. if the route the trucks took is 780 miles long, what is the speed of both trucks?

Answer 1

Let the speed of the second truck be s

Then, the speed of the first truck is 12mph faster, or s + 12

As rt = d (rate times time equals distance), or t = d/r, and it is 780 miles

the time for the second truck is 780/s and the time for the first truck is 780/(s + 12)

The first truck arrive 4 hours earlier, so the second truck takes 4 more hours.

780/s - 780/(s+12) = 4

Multiplying through by s(s+12),

780(s+12) - 780 s = 4(s)(s+12)

780s + 780 * 12 - 780s = 4s^2 + 48s

4s^2 + 48s - 9360 = 0

s^2 + 12s - 2340 = 0

(s + 6 - 6√66)(s + 6 + 6√66 ) = 0 We only take the positive value of s.

The speed of the second truck is - 6 + 6√66

he speed of the first truck is 6 + 6√66